Silvia is growing trees and studying their heights. Her data is shown below. Tree type Height (meters) Birch $3 \dfrac{1}{4}$ Spruce $2 \dfrac{7}{8}$ Oak $3 \dfrac{1}{2}$ What is the difference between the heights of the birch and spruce trees?
Explanation: The Birch tree is $3\dfrac14$ meters tall and the Spruce tree is $2\dfrac78$ meters tall. $3\frac{1}{4}$ $2\frac{7}{8}$ height of birch tree height of spruce tree difference $3\dfrac{1}{4}} - {2\dfrac{7}{8}}$ Our denominators need to be the same so we can subtract. What is the least common multiple for the denominators $D4$ and $8$ ? The least common multiple of $D4$ and $8$ is ${8}$. $\dfrac14}=\dfrac{1}{4}} \times {\dfrac{2}{2}} = \dfrac{2}{8}}$ Now, let's subtract. $\begin{aligned} &3} &\dfrac{2}{8}}\\\\ -&{2}&{\dfrac{7}{8}}\\ \hline\\ \end{aligned}$ We need to regroup $3}\dfrac{2}{8}}$ so that the fractional part is greater than ${\dfrac{7}{8}}$. $\begin{aligned} 3} \dfrac{2}{8}} &=2 + 1} \dfrac{2}{8}}\\\\ &=2} + \dfrac88} + \dfrac{2}{8}}\\\\ &=2} + \dfrac{10}{8}} \end{aligned}$ Now that our fractions have the same denominator and our first fraction is greater than our second fraction, we can subtract. $\begin{aligned} &\overset{2}}{\cancel{3}} }&\dfrac{\overset{10}}{\cancel{2}}}{8}}\\\\ -&{2}&{\dfrac{7}{8}}\\ \hline\\ &{0}&{\dfrac{3}{8}} \end{aligned}$ The difference in height between the Birch and Spruce trees is ${\dfrac{3}{8}}$ of a meter.